Physical Principles in Biology
Biology 3550
Fall 2016
Lecture 37
Review of Quiz 4
and
Molecular Motors Part 2
Monday, 28 November
c
David
P. Goldenberg
University of Utah
goldenberg@biology.utah.edu
Quiz 4: Ribulose 1,5 bisphosphate Carboxylase
2
Ribulose 1,5-bisphosphate
(RubP)
3-phosphoglycerate
(3PG)
Responsible for fixation of CO2 into carbohydrates.
Most abundant enzyme on Earth.
Quiz 4: Problem 2(a)
Calculate ∆G for reaction when concentrations are:
[3PG] = 1 mM
[RubP] = 1 mM
[CO2 ] = 8 µM
∆G = ∆G ◦ + RT ln Q
−3
2
Q=
[3PG]
=
[CO2 ][RubP]
(10
8×10−6 M × 10−3 M
2
Q=
2
M)
(1 mM)
8×10−3 mM × 1 mM
= 125
= 125
Quiz 4: Problem 2(b)
−−*
RubP + CO2 )
−− 2 3 PG
If [CO2 ] is increased from 8 µM to 250 µM, how will the
thermodynamics of the reaction change?
• ∆G
Higher concentration of reactant makes reaction more favorable,
so ∆G is more negative.
• ∆H
∆H is heat absorbed by the reaction, per mole, at constant pressure.
∆H does not depend on concentrations of reactants or products.
• ∆Ssys
∆G = ∆H − T ∆S
To make ∆G more negative, ∆S must be more positive.
An Enzyme that Moves: Adenylate Kinase
−*
ATP + AMP −
)
−− ADP + ADP
Functions to recover ATP from ADP, when ATP reserves are low.
◦
∆G ≈ 0 and Keq ≈ 1
An Enzyme that Moves: Adenylate Kinase
Open
(no substrate)
AMP
AMP + AMPPNP
2 ADP
Substrate binding induces structure to change, enclosing substrates.
Closed structure protects ATP from being hydrolyzed and releasing
phosphate.
After conversion of ATP + AMP to two ATP molecules, structure
reopens to release ADP.
An Enzyme that Moves: Adenylate Kinase
Open
(no substrate)
AMP
AMP + AMPPNP
2 ADP
What causes enzyme to move?
• Presence or absence of substrates favors different conformations.
• Weak interactions that stabilize conformations act over relatively short
distances.
• Brownian motion allows sampling of conformations.
An Enzyme that Moves: Adenylate Kinase
Open
(no substrate)
AMP
AMP + AMPPNP
2 ADP
Suppose that ATP, AMP and ADP are at equilibrium concentrations,
and ∆G = 0.
• Will the protein stop moving?
• Could the motions be used to do work?
A “Brownian Ratchet”
1
2
Thermal motions of gas molecules
in compartment 2 make paddle
wheel jiggle back and forth.
Ratchet mechanism in compartment
1 allows motion in only one
direction.
String is wound onto the pulley and
the flea is slowly lifted.
Flea
Feynman, R. P., Leighton, R. B. & Sands, M.
(2013). The Feynman Lectures on Physics,
volume I, chapter 46. Basic Books
http://www.feynmanlectures.caltech.edu/I_46.html
Will this work?
Clicker Question #3
Will the Brownian ratchet lift the flea?
1
2
1
Yes
2
Only if the temperature of
compartment 1 is greater
than that of 2.
3
Only if the temperature of
compartment 2 is greater
than that of 1.
Flea
4
No
All answers count for now.
An Enzyme that Moves: Adenylate Kinase
Open
(no substrate)
AMP
AMP + AMPPNP
2 ADP
Suppose that ATP, AMP and ADP are at equilibrium concentrations,
and ∆G = 0.
• Will the protein stop moving?
• Could the motions be used to do work?
A Hypothetical ATPase Ratchet
ATP-hydrolyzing enzyme
AT
P
Rotating wheel
Enzyme changes conformation during catalytic
cycle.
Changes in enzyme conformation control motion
of the wheel.
Steps in the cycle
ATP
1
ADP
2
ADP
Pi
3
4
5
6
Enzyme binds ATP and changes
conformation.
Wheel moves forward.
ATP is hydrolyzed and phosphate ion is
released.
Enzyme changes conformation and wheel
moves forward.
ADP is released.
Enzyme returns to original conformation
and wheel moves forward.
A Hypothetical ATPase Ratchet
ATP-hydrolyzing enzyme
AT
P
Rotating wheel
ADP
ADP
ATP
Pi
Direction of the wheel rotation is linked to
direction of catalyzed reaction:
−−−
*
ATP )
− ADP + Pi
If ATP, ADP and Pi are at equilibrium
concentrations:
∆G = 0, and wheel moves randomly in both
directions.
If ATP, ADP and Pi concentrations make ∆G < 0:
Forward reaction is favored, and wheel moves
preferentially in clockwise direction.
If ATP, ADP and Pi concentrations make ∆G > 0:
Reverse reaction is favored, and wheel moves
preferentially in counter-clockwise direction.
What if the wheel is turned by an outside force?